Christiaan J. F. van de Ven
Published 2021-09-13Version 1
In this review an overview on some recent developments on the classical limit and spontaneous symmetry breaking (SSB) in algebraic quantum theory is given. Since this algebraic approach allows for both quantum and classical theories, it is highly suitable to study the classical limit and spontaneous symmetry breaking as an emergent phenomenon when passing from the quantum realm to the classical world by switching of a semi-classical parameter. These concepts have been extensively discussed and illustrated with three different physical models: Schr\"{o}dinger operators, mean-field quantum spin systems and the Bose-Hubbard model.
Comments: 27 pages. arXiv admin note: text overlap with arXiv:2103.11914
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